Answer
$\dfrac{n(5n+9)}{2}$
Work Step by Step
We have to determine the sum:
$S=7+12+17+.....+(2+5n)$
As $12-7=17-12=...=5$, the sequence is arithmetic.
Determine its first term and the common difference:
$a_1=7$
$d=5$
The given sum contains $n$ terms; therefore we have to determine the sum of the first $n$ terms. We use the formula:
$S_n=\dfrac{n(a_1+a_n)}{2}$
$7+12+17+...+(2+5n)=\dfrac{n(7+2+5n)}{2}=\dfrac{n(5n+9)}{2}$
